[Abbaddabba]

A closer look...

Given that you have AA, there are 2 aces in the deck. Order does not matter.

2/50*1/49 of the other player holding AA, given that you have AA as well. Or 1/1225 for an individual opponent. That's what the other guy already wrote, but in terms of a ratio instead of fractions.

If you want to add another condition... that the pot is not split, you have to consider the probability of there being 4 to a flush on the board, since that's the only way that it wont be a chop. The probability of this happening is a bit more difficult to calculate. I'm not sure the exact value of how likely it is for 4 to a flush being dealt on a board.

Once you have that, the probability of it happening two times in a row is simply a matter of squaring it.